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Find link is a tool written by Edward Betts.Longer titles found: Holomorphic functional calculus (view), Antiholomorphic function (view), Formal holomorphic function (view), Milne-Thomson method for finding a holomorphic function (view), Analyticity of holomorphic functions (view)

searching for Holomorphic function 36 found (216 total)

alternate case: holomorphic function

Cartan's theorems A and B
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they imply that a holomorphic function on a closed complex submanifold, Z, of a Stein manifold X can be extended to a holomorphic function on all of X. AtList of zeta functions (354 words) [view diff] exact match in snippet view article find links to article

interval of a poset to the constant value 1. Despite not resembling a holomorphic function, the special case for the poset of integer divisibility is relatedPrime form (198 words) [view diff] exact match in snippet view article find links to article

and vanishes if and only if x = y. The prime form E is not quite a holomorphic function on X × X, but is a section of a holomorphic line bundle over thisSchottky's theorem (321 words) [view diff] exact match in snippet view article find links to article

quantitative version of Picard's theorem. It states that that for a holomorphic function f in the open unit disk that does not take the values 0 or 1, theSchottky's theorem (321 words) [view diff] exact match in snippet view article find links to article

quantitative version of Picard's theorem. It states that that for a holomorphic function f in the open unit disk that does not take the values 0 or 1, theModular lambda function (1,226 words) [view diff] exact match in snippet view article find links to article

the elliptic modular lambda function λ(τ) is a highly symmetric holomorphic function on the complex upper half-plane. It is invariant under the fractionalGeorge Adam Pfeiffer (555 words) [view diff] exact match in snippet view article find links to article

in 1943. Pfeiffer is known for publishing the first example of a holomorphic function with a non-linearizable irrational indifferent fixed point. The questionAdjunction formula (1,781 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathcal {O}}(D)} can be written as s/f, where s is a holomorphic function on U. Let η be a section over U of ωX. The Poincaré residue is thePaley–Wiener theorem (1,234 words) [view diff] exact match in snippet view article find links to article

_{0}^{\infty }F(x)e^{ix\zeta }\,dx} for ζ in the upper half-plane is a holomorphic function. Moreover, by Plancherel's theorem, one has ∫ − ∞ ∞ | f ( ξ + i ηDirichlet density (593 words) [view diff] exact match in snippet view article find links to article

pole as it has non-integral order), at least if this function is a holomorphic function times a (real) power of s−1 near s = 1. For example, if A is theEisenstein series (3,180 words) [view diff] exact match in snippet view article find links to article

converges to a holomorphic function of τ in the upper half-plane and its Fourier expansion given below shows that it extends to a holomorphic function at τ =List of mathematical functions (1,061 words) [view diff] exact match in snippet view article find links to article

of the prime p Modular lambda function, λ(τ), a highly symmetric holomorphic function on the complex upper half-plane Lamé function Mathieu function Mittag-LefflerSingular integral operators on closed curves (4,933 words) [view diff] exact match in snippet view article find links to article

proved, in a result that was a precursor of Mergelyan's theorem, any holomorphic function on Ω that extends continuously to the closure can be approximatedAppell–Humbert theorem (471 words) [view diff] exact match in snippet view article find links to article

functions on V, and for each u the expression above is a corresponding holomorphic function. The Appell–Humbert theorem (Mumford 2008) says that every line bundleMetaplectic group (1,391 words) [view diff] exact match in snippet view article find links to article

{\displaystyle g\in \mathrm {SL} _{2}(\mathbf {R} )} and ε is a holomorphic function on the upper half-plane such that ϵ ( z ) 2 = c z + d = j ( g , zGlossary of functional analysis (2,606 words) [view diff] exact match in snippet view article find links to article

states: if x is an element of a unital Banach algebra and f is a holomorphic function in a neighborhood of the spectrum σ ( x ) {\displaystyle \sigma (x)}Seiberg–Witten theory (834 words) [view diff] exact match in snippet view article find links to article

four-fermions low-energy action can be expressed in terms of a single holomorphic function F {\displaystyle {\mathcal {F}}} , as follows: The first term isBandlimiting (942 words) [view diff] exact match in snippet view article find links to article

theorem in complex analysis that says that all zeros of non-constant holomorphic function are isolated. But this contradicts our earlier finding that F 2 {\displaystyleUnified field theory (1,868 words) [view diff] exact match in snippet view article find links to article

Y + {\displaystyle Y^{+}} manifold. In mathematics, if f(z) is a holomorphic function restricted to the Real Numbers, it has the complex conjugate propertiesDenjoy–Wolff theorem (965 words) [view diff] exact match in snippet view article find links to article

Wolff. Theorem. Let D be the open unit disk in C and let f be a holomorphic function mapping D into D which is not an automorphism of D (i.e. a MöbiusConformal welding (1,123 words) [view diff] exact match in snippet view article find links to article

have smooth boundary values on the circle related by f. Since the holomorphic function on Dc vanishes at ∞, the positive powers of this pair also provideHilbert's Nullstellensatz (2,714 words) [view diff] exact match in snippet view article find links to article

{\mathcal {O}}_{\mathbb {C} ^{n},0}} is a germ represented by a holomorphic function f ~ : U → C {\displaystyle {\widetilde {f}}:U\to \mathbb {C} } ,Analytic number theory (3,518 words) [view diff] exact match in snippet view article find links to article

many cases, even where the series does not converge everywhere, the holomorphic function it defines may be analytically continued to a meromorphic functionDonald Sarason (1,205 words) [view diff] exact match in snippet view article find links to article

theorem of G. Pick on when an interpolation problem can be solved by a holomorphic function that maps the disk to itself; this is often called Nevanlinna-PickD-module (2,064 words) [view diff] exact match in snippet view article find links to article

solutions of the differential equation P f = 0, where f is some holomorphic function in C, say. The vector space consisting of the solutions of that equationNeumann–Poincaré operator (11,008 words) [view diff] exact match in snippet view article find links to article

=\,\,\int _{|z|=R}\partial _{n}u.}} At ∞ u is the real part of a holomorphic function F with F ( z ) = a 0 + a 1 z − 1 + a 2 z − 2 + ⋯ {\displaystyle \displaystyleDifferential forms on a Riemann surface (11,032 words) [view diff] exact match in snippet view article find links to article

1-forms locally have the form df with f a holomorphic function and since the real part of a holomorphic function is harmonic, harmonic 1-forms locally haveHodge star operator (5,108 words) [view diff] exact match in snippet view article find links to article

invariant under holomorphic changes of coordinate. If z = x + iy is a holomorphic function of w = u + iv, then by the Cauchy–Riemann equations we have thatSeries (mathematics) (8,592 words) [view diff] exact match in snippet view article

absolutely when Re s > 1, but the zeta function can be extended to a holomorphic function defined on C ∖ { 1 } {\displaystyle \mathbf {C} \setminus \{1\}}Hypergeometric function (7,016 words) [view diff] exact match in snippet view article find links to article

there are usually two special solutions of the form xs times a holomorphic function of x, where s is one of the two roots of the indicial equation andWigner quasiprobability distribution (4,602 words) [view diff] exact match in snippet view article find links to article

) = e g ( x + i p ) {\displaystyle F(x+ip)=e^{g(x+ip)}} for some holomorphic function g {\displaystyle g} . But in order for F {\displaystyle F} to belongModuli stack of elliptic curves (2,346 words) [view diff] exact match in snippet view article find links to article

\right)=(c\tau +d)^{k}f(\tau )} This is exactly the condition for a holomorphic function to be modular. The modular forms are the modular functions whichKnizhnik–Zamolodchikov equations (2,968 words) [view diff] exact match in snippet view article find links to article

correlation function can be analytically continued as multi-valued holomorphic function to the domain X n ⊂ C n {\displaystyle X_{n}\subset \mathbb {C} ^{n}}Generalized conic (2,764 words) [view diff] exact match in snippet view article find links to article

in the theory of approximation. The polynomial approximation of a holomorphic function can be interpreted as the approximation of the level curves withPlanar Riemann surface (3,689 words) [view diff] exact match in snippet view article find links to article

Let X be a Riemann surface and W an open connected subset with a holomorphic function g = u + iv differing from f by a constant such that g(W) lies inSingular integral operators of convolution type (12,875 words) [view diff] exact match in snippet view article find links to article

on H in the following sense: f is in H2 provided that there is a holomorphic function F(z) on H such that the functions fy(x) = f(x + iy) for y > 0 are